CAS
w
Math
Factoring Polynomials
monomials
don’t factor
difference
a2–b2 =
(a+b)(a-b)
sum
can’t factor
two perfect
squares
binomials
difference
a3–b3 =
(a–b) (a2+ab+b2)
sum
a3+b3 =
(a+b) (a2–ab+b2)
two perfect
cubes
Factoring
Polynomials
Factor out
any GCF
perfect square
trinomial
a2+2ab+b2=(a+b)2
trinomials
generic
trinomial
ax2+bx+c
polynomials
with four or more
terms
factor by grouping–
find two numbers (b1, b2) that “multiply” to the
value of ac and add up to the
value of b ax2+b1x+b2x+c
factor by grouping –
factor into two groups so that the groups
have a common factor
Before beginning to factor by any of the methods below, check to see if each term of your
polynomial has a common factor that you factor out.
Difference of Two Squares:
a2 – b2 = (a + b) (a – b)
Difference of Two Cubes: a3 – b3 = (a – b) (a2 + ab + b2)
Sum of Two Cubes:
a3 + b3 = (a + b) (a2 - ab + b2)
Quadratics:
Ax2 + Bx + C = (ax + b) (cx + d)
• A = ac
• B = ad + bc
• C = bd
Ax2 – Bx + C = (ax – b) (cx – d)
• A = ac
• B = ad + bc
• C = bd
CAS
Ax2 + Bx – C = (ax + b) (cx – d)
• A = ac
• B = bc – ad, where bc > ad
• C = bd
Ax2 – Bx – C = (ax + b) (cx – d)
• A = ac
• B = ad – bc, where ad > bc
• C = bd
Quadratic Formula:
For Ax2 + Bx + C = 0
x = -B ± (B2 – 4AC)
2A
Factoring by Grouping:
Ax3 + Bx2 + Cx + D = ax2 (cx + d) + b (cx + d) = (ax2 + b) (cx + d)
w
Math